I ALWAYS go to regional theatre by myself, unless I KNOW my partner will like it. She is not a big theatre person, but I have brought her to enough shows where I know what she likes and doesn't like.
Plus you get all those cool, random single seats with great views.
I've also met some amazing people. I actually got to go backstage once because the woman next to me had a single seat as well, away from her friends because she bought them at a different time, and she knew the people on stage and we struck up a conversation and she liked what I did for a living!
I am also the biggest introvert ever, so the more alone I am the more I can actually get into the show I am seeing without worrying about what my friends are thinking about the show.
As for Broadway, because I don't live in the state, my close friend and I take trips together to shows. It helps because we rush and we usually have a third wheel join us once we are in the City.